SOLUTION: http://i42.tinypic.com/294h0m0.jpg <-------Equations picture is in there please show work would appreciate it thanks

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Question 189374: http://i42.tinypic.com/294h0m0.jpg <-------Equations picture is in there
please show work would appreciate it thanks
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(2/3x) - 3 = 3/(x+3)
(2-9x)/3x = 3/(x+3)
cross multiply
(2-9x)*(x+3) = 9x
-9x%5E2+-+25x+%2B+6+=+9x
9x%5E2+%2B+34x+-+6+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B34x%2B-6+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2834%29%5E2-4%2A9%2A-6=1372.

Discriminant d=1372 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-34%2B-sqrt%28+1372+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2834%29%2Bsqrt%28+1372+%29%29%2F2%5C9+=+0.168917686383571
x%5B2%5D+=+%28-%2834%29-sqrt%28+1372+%29%29%2F2%5C9+=+-3.94669546416135

Quadratic expression 9x%5E2%2B34x%2B-6 can be factored:
9x%5E2%2B34x%2B-6+=+%28x-0.168917686383571%29%2A%28x--3.94669546416135%29
Again, the answer is: 0.168917686383571, -3.94669546416135. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B34%2Ax%2B-6+%29